# Modules

## Core modules

### Semester 2

- Algebras and Representation Theory
- Elliptic and Parabolic PDEs
- Functional Analysis
- Manifolds
- Mathematical Biology and Physiology
- Modern Regression and Bayesian Methods
- Numerical Methods
- Stochastic Processes

### Semester 1

- Algebraic Topology
- Asymptotic and Analytical Methods
- Continuum Mechanics
- Dynamical Systems and Conservation Laws
- Foundations of Probability
- Groups, Rings and Modules
- Measure and Integration
- Regression and Simulation Methods

## Supplementary modules

### Semester 1

- Ethics in Mathematics
- Galois Theory of Commutative Rings
- Advanced PDE I
- Convergence of Probability Measures and its Applications
- Stochastic PDEs: Applications and Numerics

### Semester 2

### Previous supplementary modules

These modules ran previously, and are not currently running in this session.

- Advanced PDE I
- Advanced PDE II
- Analysis and Numerics of Stochastic PDEs
- Category Theory
- Central simple algebras and Galois cohomology
- Diffusion Processes
- Geometric Measure Theory
- Harmonic Analysis
- Homogenisation
- Homogenisation I
- Homogenisation II: Stochastic Problems
- Homotopical Ideas in Topology and Beyond
- Integrability and Representation Theory
- Markov Chain Monte Carlo Methods (MCMC)
- Modern Topics in Quantum Integrable Systems
- Spectral Theory and Differential Operators
- Stochastic Integration
- Stochastic PDEs
- Stochastic PDEs and their Applications
- Stochastic Stability
- The mod 2 Steenrod Algebra in Theory and in Practice
- Topics in Algebra, Geometry and Mathematical Physics
- Variational methods for PDEs
- What is Numerical Analysis?
- Working Seminar on Finite-Dimensional Algebras